Question
The average score of 'x' boys is (x + 5), and the
average score of 30 girls is (3x - 10). If the combined average score of all students is 60, then find the number of boys.Solution
ATQ; [x × (x + 5) + 30 × (3x - 10)] ÷ (x + 30) = 60 Or, x² + 5x + 90x - 300 = 60x + 1800 Or, x² + 35x - 2100 = 0 Or, x² + 70x - 35x - 2100 = 0 Or, x(x + 70) - 35(x + 70) = 0 Or, (x + 70)(x - 35) = 0 So, x = 35 or -70 Since number of boys can't be negative, x = 35
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